Daily Practice · Higher Plus

April 1956 5-a-day

← Today's Higher Plus sheet

April 1956

30 sheets · 150 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' April 1956 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in April 1956

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st April 1956The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
  2. 2nd April 1956A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
  3. 3rd April 1956On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  4. 4th April 1956A rectangle is 18 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
  5. 5th April 1956Write 2/(x - 6) + 7/(x + 5) as a single fraction.
  6. 6th April 1956A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
  7. 7th April 1956In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
  8. 8th April 1956The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
  9. 9th April 1956A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
  10. 10th April 1956Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
  11. 11th April 1956Solve 4x^2 + 8x - 5 = 0.
  12. 12th April 1956y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
  13. 13th April 1956In a vector proof you find that vector PQ = 4a - 4b and vector RS = 12a - 12b. What does this show about PQ and RS?
  14. 14th April 1956A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
  15. 15th April 1956On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  16. 16th April 1956A block has mass 730 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  17. 17th April 1956f(x) = 3x - 10. Work out the inverse function f^-1(x).
  18. 18th April 1956y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
  19. 19th April 1956A cuboid measures 8 cm by 13 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  20. 20th April 1956A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  21. 21st April 1956A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
  22. 22nd April 1956x = 85 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
  23. 23rd April 1956Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
  24. 24th April 1956y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 25.
  25. 25th April 1956A cuboid measures 12 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  26. 26th April 1956A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  27. 27th April 1956On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  28. 28th April 1956A car covers 650 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  29. 29th April 1956Use the iteration x(n+1) = cube root of (7x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
  30. 30th April 1956A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.

The same month at another level